Suppose the production function for good q is given by q=3 ∙K+2∙ L where K and L are capital and labor inputs. Consider three statements about this function: I. The function exhibits constant returns to scale II. The function exhibits diminishing marginal productivities to all inputs III. The function has a constant marginal rate of technical substitution

Suppose the production function for good q is given by q=3 ∙K+2∙ L where K and L are capital and labor inputs. Consider three statements about this function: I. The function exhibits constant returns to scale II. The function exhibits diminishing marginal productivities to all inputs III. The function has a constant marginal rate of technical substitution

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.9P

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6. Which of the following are true (check all that apply) Note: IRTS=increasing returns to scale, CRTS=constant returns to scale, DRTS=decreasing returns to scale a. if the production function exhibits IRTS, then the cost function will exhibit economies of scale b. if the production function exhibits IRTS, then the cost function will exhibit diseconomies economies of scale c. if the cost function exhibits diseconomies of scale, then the producing function exhibits DRTS d. if the production function exhibits CRTS, then the cost function will exhibit constant economies of scale e. if the production function exhibits DRTS then the cost function will exhibit diseconomies of scale
1.Suppose a chair manufacturer is producing in the short run (with its existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:Number of Workers Number ofChairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to becomenegative.
3. Consider the following production functions along with their corresponding marginal product of labor function. I. Q = 15KL II. Q = 2K0.4L0.6 III. Q = 8K + L. a. In each case, what happens to the marginal product of labor as the firm uses more labor? b. In each case, what happens to the marginal product of labor as the firm uses more capital?
2. Suppose a firm’s production function is given as; Y= { xa1 x1-a2}i.Derive the marginal rate of technical substitution ii.Does the function exhibit diminishing marginal returns?
A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $45 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour? Capital decreases and labor increases. Capital and labor increase. It does not change. Capital increases and labor decreases. Only typed answer
A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3? unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour? (Choose one that is the best answer) Capital decreases and labor increases. It does not change. Capital increases and labor decreases. Capital and labor increase.
A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour?multiple choice Capital and labor increase. Capital decreases and labor increases. Capital increases and labor decreases. It does not change.
QUESTION 1 Consider the following production functions, where q is the quantity produced of the good, Kis the quantity of capital used, and L is the quantity of labor used:Production function 1q (K, L) = K^αL^βProduction function 2q (K, L) = K^α + L^βa) What is production function? Explain by providing appropriate graph.b) Does Production function 1 have decreasing, constant, or increasing returns to scale?Explain.c) Suppose that α = 1 and β = 1. Does Production function 2 have decreasing, constant,or increasing returns to scale? Explain.d) Suppose that α = 1/2 and β = 1/2. Does Production function 1 have decreasing,constant, or increasing returns to scale? Explain
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1.A 15 per cent increase in all inputs leads to only a 5 per cent increase in the output. Are the returns to scale increasing, constant or diminishing? Illustrate your answer2.What is the slope of an iso-cost line equal to and why? Provide mathematical explanation3.“By definition, cost is zero if a firm does not hire any input. Hence cost-minimization essentially means shutting down the operation of the firm.” Do you agree with the statement? Justify you answer by giving an explanation from microeconomic theory.4.What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.
7 Define the cost function c(w1,w2 ,y) =w1x1(w1,w2,y) + w2x2(w1,w2,y). Show that the cost function is homogeneous of degree one and concave in ( w1, w2) .
1. Suppose the production function is Q = 8L + 15K where Q is the quantity of output, L is the quantity of labor used in production, and K is the quantity of capital used in production. What can be said about this production function? It has Decreasing Returns to Scale It has Constant Returns to Scale It has Increasing Returns to Scale There isn’t enough information to determine the Returns to Scale for this production function 2. You’re dreaming of what to do during a nice summer day. You could mow the lawn which you would pay someone $15 to do for you. You could go for a walk which you value at $11. You could also take a nap and ignore everyone and everything else which you would pay $29 to do. If you to take a nap, what is your opportunity cost? Group of answer choices $29 $26 $15 $11